Heat oil in a wok or large skillet over medium-high heat. Once oil is hot, add shallot, peppers, and minced garlic, stir frying for 30 seconds, until fragrant and light golden.
Add the chicken. Season with salt and pepper, and stir fry for 5-6 minutes, stirring often, until browned and mostly cooked.
While the chicken cooks, combine the sauce ingredients in a small bowl and whisk well.
Add the whites of the green onion and 1 cup of rice, stir frying for 20-30 more seconds.
Move everything to one side of the cooking surface. Pour the whisked egg onto the other side, stirring and folding for 1-2 minutes, until scrambled. Stir it in with the rice mixture.
Add the sauce to the pan and stir well, then add in the rest of the cooked rice and green parts of green onion. Stir fry everything for another 2-3 minutes until warmed through and well mixed, tasting and adjusting seasoning and heat as desired. Stir in the basil, remove from the heat, then serve with lime wedges and more basil.